A video game developer is interested in comparing the completion time for a single level of their new game on easy mode as opposed to difficult mode (Note: the game is the same in both cases, but in difficult mode it is harder to defeat enemies). The researchers want to know if it will take individuals longer to complete the difficult mode than it would to complete the easy mode. They randomly selected 50 individuals of varying gaming experience. The researchers proposed three possible designs:

a. Randomly assign individuals into either the easy or difficult group, and compare their overall times (with 25 individuals in each group).

b. Pair individuals based on their gaming experience level, randomly assign one individual from each pair to complete the easy version and the other to complete the hard version. Evaluate the difference in time for each pair, and take an overall mean.

c. Have each individual complete the game twice: once on easy mode and once on hard mode. Evaluate the difference in time for each player, and take an overall mean.

1(a)

What type of design is design (a)?

(ex. one mean, one proportion, two means, two proportions, matched pairs, repeated measures, regression)

1(b)

What type of design is design (b)?

(ex. one mean, one proportion, two means, two proportions, matched pairs, repeated measures, regression)

1(c)

What type of design is design (c)?

(ex. one mean, one proportion, two means, two proportions, matched pairs, repeated measures, regression)

1(d)

Which design would work best in this case? Explain.

2.

The researchers have decided to conduct the study twice: once with method a, and once with method b (from above). The following questions will address the first method:

Randomly assign individuals into either the easy or difficult group, and compare their overall times (with 25 individuals in each group).

2(a)

State the null and alternative hypothesis insymbols.

2(b)

What are the observational units in this experiment?

2(c)

The mean completion time for the easy level was 60 minutes, with a standard deviation of 10 minutes. The mean completion time for the difficult level was 90 minutes, with a standard deviation of 20 minutes. The distribution of the results is not strongly skewed.

2(c) i

Can the theory based approach be used in this situation? Why or why not?

2(c) ii

Calculate the Standard Error. Show your work.

2(c) iii

Calculate the Standardized Statistic. Show your work.

2(c) iv

Interpret the meaning of the standardized statistic in the context of the problem.

2(c) v

Would you reject or fail to reject the null? Why?

2(c) vi

Based on your standardized statistic, state your conclusion in the context of the problem.